Problem: Simplify the following expression: $z = \dfrac{y}{10} - \dfrac{7y}{8}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $10$ and $8$ $\lcm(10, 8) = 40$ $ z = \dfrac{4}{4} \cdot \dfrac{y}{10} - \dfrac{5}{5} \cdot \dfrac{7y}{8} $ $z = \dfrac{4y}{40} - \dfrac{35y}{40}$ $z = \dfrac{4y -35y}{40}$ $z = \dfrac{-31y}{40}$